Algorithm for computation of Zernike polynomials expansion coefficients

Details Algorithm for computation of Zernike polynomials expansion coefficients Algorithm for computation of Zernike polynomials expansion coefficients

Feb 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989apopt..28..749p&link_type=abstract

Applied Optics, Volume 28, Issue 4, February 15, 1989, pp.749-754

Physics

Optics

6

Diffraction, Aberrations, Image Evaluation, Modulation Transfer Function, Optical Transfer Function, Optical Testing, Optical Design

Scientific paper

A numerically efficient algorithm for expanding a function in a series of Zernike polynomials is presented. The algorithm evaluates the expansion coefficients through the standard 2-D integration formula derived from the Zernike polynomials' orthogonal properties. Quadratic approximations are used along with the function to be expanded to eliminate the computational problems associated with integrating the oscillatory behavior of the Zernike polynomials. This yields a procedure that is both fast and numerically accurate.

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